用温和几何理论解释深度学习模型的收敛性，为AI提供数学新视角。
Deep Learning as the Disciplined Construction of Tame Objects
- 将深度学习视为温和几何中的函数组合，构建理论框架。
- 在非光滑非凸但温和条件下，给出随机梯度下降的收敛保证。
- 适合对深度学习理论和数学基础感兴趣的学者与研究者。
可将深度学习模型视为所谓温和几何中函数的复合。本文综述了温和几何（又称o-极小性）、优化理论与深度学习理论实践交汇处的一些主题。通过逐步引入构建一般非光滑非凸但温和设置下随机梯度下降收敛保证的概念与工具，展示了温和几何作为人工智能系统研究——尤其是深度学习——的自然数学框架的潜力。
原文摘要 · Abstract (English)
One can see deep-learning models as compositions of functions within the so-called tame geometry. In this expository note, we give an overview of some topics at the interface of tame geometry (also known as o-minimality), optimization theory, and deep learning theory and practice. To do so, we gradually introduce the concepts and tools used to build convergence guarantees for stochastic gradient descent in a general nonsmooth nonconvex, but tame, setting. This illustrates some ways in which tame geometry is a natural mathematical framework for the study of AI systems, especially within Deep Learning.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。